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Using a validation set to monitor the convergence of the fugw loss#

In this example, we use 3 fMRI feature maps for training and 2 independant fMRI feature maps for testing to examine the evolutions of a training and a validation loss on 2 low-resolution brain volumes.

import numpy as np
import matplotlib.pyplot as plt

from nilearn import datasets, image, plotting
from scipy.spatial import distance_matrix
from fugw.mappings import FUGW

We first fetch 5 contrasts for each subject from the localizer dataset.

n_subjects = 2

contrasts = [
    "sentence reading vs checkerboard",
    "sentence listening",
    "calculation vs sentences",
    "left vs right button press",
    "checkerboard",
]
n_training_contrasts = 3

brain_data = datasets.fetch_localizer_contrasts(
    contrasts,
    n_subjects=n_subjects,
    get_anats=True,
    get_masks=True,
)

source_imgs_paths = brain_data["cmaps"][0 : len(contrasts)]
target_imgs_paths = brain_data["cmaps"][len(contrasts) : 2 * len(contrasts)]
source_mask = brain_data["masks"][0]

source_im = image.load_img(source_imgs_paths)
target_im = image.load_img(target_imgs_paths)
mask = image.load_img(source_mask)

/usr/local/lib/python3.8/site-packages/nilearn/datasets/func.py:893: UserWarning:

`legacy_format` will default to `False` in release 0.11. Dataset fetchers will then return pandas dataframes by default instead of recarrays.

We then downsample the images by 5 to reduce the computational cost.

SCALE_FACTOR = 5

resized_source_affine = source_im.affine.copy() * SCALE_FACTOR
resized_target_affine = target_im.affine.copy() * SCALE_FACTOR

source_im_resized = image.resample_img(source_im, resized_source_affine)
target_im_resized = image.resample_img(target_im, resized_target_affine)
mask_resized = image.resample_img(mask, resized_source_affine)

source_maps = np.nan_to_num(source_im_resized.get_fdata())
target_maps = np.nan_to_num(target_im_resized.get_fdata())
segmentation = mask_resized.get_fdata()

coordinates = np.argwhere(segmentation > 0)

source_features = source_maps[
    coordinates[:, 0], coordinates[:, 1], coordinates[:, 2]
].T
target_features = target_maps[
    coordinates[:, 0], coordinates[:, 1], coordinates[:, 2]
].T

fig = plt.figure()
ax = fig.add_subplot(projection="3d")
ax.scatter(coordinates[:, 0], coordinates[:, 1], coordinates[:, 2], marker="o")
ax.view_init(10, 135)
# make the panes transparent
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
# make the grid lines transparent
ax.xaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.yaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.zaxis._axinfo["grid"]["color"] = (1, 1, 1, 0)
ax.set_title("3D voxel coordinates")
plt.show()
3D voxel coordinates
/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:673: RuntimeWarning:

NaNs or infinite values are present in the data passed to resample. This is a bad thing as they make resampling ill-defined and much slower.

/usr/local/lib/python3.8/site-packages/nilearn/image/resampling.py:294: UserWarning:

Resampling binary images with continuous or linear interpolation. This might lead to unexpected results. You might consider using nearest interpolation instead.

We then compute the distance matrix between voxel coordinates.

source_geometry = distance_matrix(coordinates, coordinates)
target_geometry = source_geometry.copy()

In order to avoid numerical errors when fitting the mapping, we normalize both the features and the geometry.

source_features_normalized = source_features / np.linalg.norm(
    source_features, axis=1
).reshape(-1, 1)
target_features_normalized = target_features / np.linalg.norm(
    target_features, axis=1
).reshape(-1, 1)
source_geometry_normalized = source_geometry / np.max(source_geometry)
target_geometry_normalized = target_geometry / np.max(target_geometry)

We now fit the mapping using the sinkhorn solver and 10 BCD iterations. We use the first 3 feature maps for training and the last 2 for validation. Anatomical kernels are kept identical for both training and validation, as it will usually be the case in practice when aligning real fMRI data.

mapping = FUGW(alpha=0.5, rho=1, eps=1e-4)
_ = mapping.fit(
    source_features=source_features_normalized[:n_training_contrasts],
    target_features=target_features_normalized[:n_training_contrasts],
    source_geometry=source_geometry_normalized,
    target_geometry=target_geometry_normalized,
    source_features_val=source_features_normalized[n_training_contrasts:],
    target_features_val=target_features_normalized[n_training_contrasts:],
    solver="sinkhorn",
    solver_params={
        "nits_bcd": 10,
    },
    verbose=True,
)

[20:55:44] Validation data for anatomical kernels is not provided.  dense.py:226
           Using training data instead.


[20:55:54] BCD step 1/10   FUGW loss:      0.02483261190354824      dense.py:521
           Validation loss:        0.02661210484802723


[20:56:12] BCD step 2/10   FUGW loss:      0.007542587351053953     dense.py:521
           Validation loss:        0.007889988832175732


[20:56:30] BCD step 3/10   FUGW loss:      0.006806590594351292     dense.py:521
           Validation loss:        0.006886965595185757


[20:56:49] BCD step 4/10   FUGW loss:      0.006415019743144512     dense.py:521
           Validation loss:        0.006309802178293467


[20:57:07] BCD step 5/10   FUGW loss:      0.0062031010165810585    dense.py:521
           Validation loss:        0.005970505066215992


[20:57:25] BCD step 6/10   FUGW loss:      0.0059886109083890915    dense.py:521
           Validation loss:        0.005597996059805155


[20:57:44] BCD step 7/10   FUGW loss:      0.005855436436831951     dense.py:521
           Validation loss:        0.0053308987990021706


[20:58:02] BCD step 8/10   FUGW loss:      0.005845545791089535     dense.py:521
           Validation loss:        0.005313204135745764


[20:58:21] BCD step 9/10   FUGW loss:      0.005844415631145239     dense.py:521
           Validation loss:        0.005311452783644199


[20:58:39] BCD step 10/10  FUGW loss:      0.005844208877533674     dense.py:521
           Validation loss:        0.005310453474521637

Plot the evolution of losses on train and test datasets.

fig, ax1 = plt.subplots()
ax1.set_xlabel("BCD Step")
ax1.set_ylabel("FUGW loss", color="black")
ax1.tick_params(axis="y", labelcolor="black")

ax1.plot(mapping.loss_steps, mapping.loss["total"], color="blue")
ax1.plot(mapping.loss_steps, mapping.loss_val["total"], color="red")

plt.title("Training and validation losses")
plt.legend(["Train", "Validation"])
fig.tight_layout()  # otherwise the right y-label is slightly clipped
plt.show()
Training and validation losses

Plot the alignment of the second validation feature map and project it on the fsaverage5 surface.

example_array = np.nan_to_num(source_im_resized.slicer[..., -1].get_fdata())
example_array /= np.max(np.abs(example_array))
example = image.new_img_like(source_im_resized, example_array)
plotting.view_img_on_surf(example, threshold="50%", surf_mesh="fsaverage5")


Total running time of the script: ( 2 minutes 58.448 seconds)

Estimated memory usage: 11 MB

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